MPM2D
Finding Equation of a Parabola
In this course we have looked at quadratic equations in 3 different forms.
Standard form
Factored form
Vertex Form
To determine the equation of a parabola given a graph you can would most likely use factored form or
vertex form (depending on what you know about the graph).
Example
Find an equation for the graph below.
Example - A soccer ball is kicked from the ground. After travelling a horizontal distance of 35 m it just
passes over a 1.5m tall fence before hitting the ground 37 m from where it was kicked.
Sketch the graph of the ball. Find an equation that relates the height of the ball to the horizontal
distance it has travelled.
Finding the Equation of a Quadratic Relationship - Problem Set
1. Find the equation of each of the parabolas below.
a)
b)
2. Below is a photograph of the Sydney Harbour Bridge. The lower arch is parabolic in shape. In
this problem you will model this shape with a quadratic equation.
The lower arch has a span (horizontal length) of 503 m and touches the water at each end. The bridge is
50m above the water. The bridge meets the lower arch at a horizontal distance of 60m from the start of
the bridge.
a) Use the information above to find an equation for the lower arch.
b) Find the maximum height (From the water level) of the lower arch.
ANSWERS
1. a) 𝑦 =
−5
(𝑥
4
−5
− 1)2 + 3
2. a) 𝑦 = 2658 𝑥(𝑥 − 503)
b) y = -2(x-1)(x+2)
b) 119m